I have a Mesh with an Armature. The Mesh has a "Mesh Deform" modifier, which itself has physics. Why does it break when Rendered?
I'm an idiot! I tried everything, consumed pages of archaic documents on modifiers, I dug all the way over to page THREE of google search results, I lost hours of sleep, watched an embarrassing amount of tangentially related tutorial videos in which the teacher, bless them, had to communicate through a thoroughly mashed potato they had stuck two wires into,
...the solution was to update Blender. SMH. I can't believe I forgot.
For future reference, the above set-up works! If anyone in the future is having trouble figuring out Mesh Deform with Armatures, I hope these pictures and descriptions help. Just... make sure you've updated blender. Lord.
And make sure you Bake any physics or wiggle bones before rendering, as always.